Description
Calculate one probability-weighted incentive contribution for a correlated recommendation.
Game-theoretic calculations depend on specified players, actions, payoff direction, probabilities and continuation assumptions. A single incentive term, coalition inequality or candidate best response is only part of a complete equilibrium argument. Supplied preferences and payoffs are model inputs rather than observed behavior or a moral allocation rule.
Calculate one probability-weighted incentive contribution for a correlated recommendation.
When to use this tool
Use Two Player Correlated Recommendation Incentive Term when checking the stated local payoff, strategy, matching or repeated-game condition.
How to use the tool and how it works
- Enter jointRecommendationProbability, obeyPayoff, deviationPayoff. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read incentiveContribution. Use the output convention below.
Require jointRecommendationProbability in [0,1]. Return probability*(obeyPayoff-deviationPayoff) as one incentive contribution.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| jointRecommendationProbability | Joint probability for one recommendation cell, rather than a normalized conditional probability. | Required. Finite number; minimum 0; maximum 1. |
| obeyPayoff | Obey Payoff | Required. Finite number. |
| deviationPayoff | Deviation Payoff | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| incentiveContribution | Incentive Contribution | Required. Finite number. |
{
"input": {
"jointRecommendationProbability": 0.25,
"obeyPayoff": 8,
"deviationPayoff": 4
},
"output": {
"incentiveContribution": 1
}
}Limitations and assumptions
- Probability is a joint recommendation weight, not an automatically normalized conditional probability; one term does not establish correlated equilibrium.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete game, feasible strategy space and justified information/continuation assumptions for equilibrium, welfare or actual decision analysis.
References
Similar or alternative tools
- Strategy Deviation Regret
Calculate a strategy-deviation gain and its nonnegative regret component.
- Repeated Game Deviation Deterrence Gap
Check a normalized repeated-game deviation inequality under a constant punishment continuation.